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In a text I'm composing I try to explain that there are two kinds of definitions:

The first one is the kind where you explain the characteristics of an element that belongs to a set:
"A crestboot is a kind of boot that has this, this, and that characteristics".

The second one is given in terms of belonging to other known sets:
"A frumboot is a either a snaboot or a fluiboot".

Is there a word or phrase that can be used to refer to each of these kinds of definitions? I was thinking something like "descriptive definition" and "compositive definition".

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In set theory there are intensional definitions and extensional definitions:

an intensional definition of bachelor is 'unmarried man'. Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor

That sounds like how you want to define your crestboot.

an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.

That sounds like what you're trying to get at with the frumboot.

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  • This seems to be precisely what I was looking for; do you believe the average programmer or computer scientist would know what those terms mean?
    – rick
    Sep 4, 2014 at 15:45
  • It seems like enumerative definition is a special case of extensional definition where you exhaust all the possible values. This would sound familiar to programmers.
    – rick
    Sep 4, 2014 at 15:48
  • @rick They're established words. I wouldn't worry about using them if they are what you need; people can look them up and you can include definitions if you have worries about whether your audience has heard them before. And as words go for what they are, they seem all right to me.
    – HostileFork says dont trust SE
    Sep 4, 2014 at 15:54

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